I'd like to think of it this way: execution is the active searching of the problem space until you find a local maxima. The idea is only the starting point.

Sure, you can get lucky and find an idea that is already on a local maxima - but you wouldn't know that without verifying.

Simply thinking "what if you sold socks that didn't match?" is far from enough to prove that it's a good idea. If you gave it just five minutes you would probably come up with a hundred similar seemingly weird ideas.

Some examples:

What if TVs were not boxes but bubble-shaped?

What if cars bounced like rubber balls? Would that make them safer?

What if pants had four legs? Of different lengths.

What if shoes were glued together?

What if I had an internet connected computer in my sight of vision constantly? (This will happen, we all know that.)

What if books never ended?

What if people could grow all their food, including meat, at home, in a box like a micro oven?

I can go on like this forever. How do I know which ideas are the good ones?

By testing them in the real world - searching the problem space for a local maxima - that's the only way. And that takes execution and effort.

"Execution is everything" is not tautological. It's not saying "execution is necessary" — it's saying that how you execute makes an order of magnitude greater difference than what idea you pick. Good execution will save all but the worst ideas, but an amazing idea will still fail if not executed well.

For example, Apple's Newton PDA: Great idea — it caught on like wildfire when Palm did the same thing a few years later. But it flopped when Apple did it, because Apple's execution was flawed.